When you mean offshore what do you mean? Because we don't know where you are, so offshore means another country for everyone else. So if you are not in the US, then a US server is actually offshore for you.
I was just popping in to basically say what nibb said. However, presuming you mean somewhere offshore of the USA, then I have friends who work in certain industries (you know the ones) that use www.securehost.com . Their servers are all on Caribbean islands (mainly former British colonies like Jamaica).
Does it need to be literally offshore, or can it be in Canada? People think that Canada is within US jurisdiction, but if any indication that they do not like using KLOUD(the word for fluffballs in the sky gets filtered for me...a lot of words get filtered...) much because the United States basically said the cloud is their's, I believe Canadian hosting is safe. Try to stay away from hosting in India, hackers and low speed. A UK is actually pretty darn good, but I tend to stay away just because I figure they have a very close relationship with US, and if I'm using a UK server to do somethng I can't do on a US server...I get antsy and think that I might still get in trouble (though I won't...) Antigua/Barbuda/Cyprus/Malta/Switzerland/Netherlands/Finland/Sweden are excellent locations to host a site....I guess basically think of a foreign destination where you'd like to fantasize having a perfect vacation at and use that place for hosting
What is the reason for needing this type of hosting? What do you mean by "offshore", where are you located? There isn't really enough information to give a good answer here.